Thank you for the great answers. They solved my issue.
So, the main problem was that I did not understand that the settings under Tools | Options | Tags | Mpeg apply to different types of operations. I think it would be great if the docs under /Mp3tag/help/options_id3.html would be updated to accommodate morons like myself. My suggestion would be to add some more text in each section (Read, Write and Remove) describing to which operations (Such as Cut / Paste / Remove), the settings in each section apply.
Also, and I realize that this would trip up everyone that are already familiar with this excellent app, I think that Save tag should be modified, or have an option added, to be able to implicitly remove tags. The reasoning is that I think that in general, people want their music collection to have uniform tags. So having Save tag automatically create and remove tags in such a way that the end result is the same for each song regardless of which tags were present before, would be a good thing.
@JJ Johnson, am I understanding correctly that, like me, you were not aware of the Edit | Remove command and its relationship with the Tags | Mpeg | Remove settings? Though, even with Edit | Remove available, I think your procedure #2 is still required so that information in the tags is not lost in the case of the user wanting ID3v1 tags, the song having only ID3v2 tags and Tags | Mpeg | Remove having been configured to remove ID3v2.